If the universal U -1- 2- 3- 4- 5- 6- 7 - A - - 1- 2- 5- 7 - - B - -3- 4- 5- 6- Verify left- Acup B right- -A-cap B-

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Given- universal set- U-1-2-3-4-5-6-7-A-1-2-5-7-B-3-4-5-6-A-x222A-B-x2032-U-x2212-A-x222A-B-1-2-3-4-5-6-7-x2212-1-2-3-4-5-6-7-x3D5-A-x2032-x2229-B-x2032-U-x2212-A-n-U-x2212-B-3-4-6-n-1-2-7-x3D5-Hence -A-x222A-B-x2032-A-x2032-x2229-B-x2032-

If the universal set $U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 5, 7}, B = {3, 4, 5, 6}$ . Verify ${(A \cup B)}^{'} = A^{'} \cap B^{'}$

Given, universal set, $U = {1, 2, 3, 4, 5, 6, 7}$
$A = {1, 2, 5, 7}$
$B = {3, 4, 5, 6}$
$(A \cup B)^{'} = U - (A \cup B)$
$= {1, 2, 3, 4, 5, 6, 7} - {1, 2, 3, 4, 5, 6, 7}$
$= ϕ$
$A^{'} \cap B^{'} = (U - A) n (U - B)$
$= {3, 4, 6} n {1, 2, 7}$
$= ϕ$
Hence $(A \cup B)^{'} = A^{'} \cap B^{'}$ .

If the universal set U={1,2,3,4,5,6,7},A={1,2,5,7},B={3,4,5,6}. Verify (A∪B)′=A′∩B′

Given, universal set, U={1,2,3,4,5,6,7}A={1,2,5,7}B={3,4,5,6}(A∪B)′=U−(A∪B)={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕA′∩B′=(U−A)n(U−B)={3,4,6}n{1,2,7}=ϕHence (A∪B)′=A′∩B′.

If the universal set $U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 5, 7}, B = {3, 4, 5, 6}$ . Verify ${(A \cup B)}^{'} = A^{'} \cap B^{'}$

Given, universal set, $U = {1, 2, 3, 4, 5, 6, 7}$
$A = {1, 2, 5, 7}$
$B = {3, 4, 5, 6}$
$(A \cup B)^{'} = U - (A \cup B)$
$= {1, 2, 3, 4, 5, 6, 7} - {1, 2, 3, 4, 5, 6, 7}$
$= ϕ$
$A^{'} \cap B^{'} = (U - A) n (U - B)$
$= {3, 4, 6} n {1, 2, 7}$
$= ϕ$
Hence $(A \cup B)^{'} = A^{'} \cap B^{'}$ .